The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1 2X+2  2  1  1 X+2  1 3X+2  1  2  1  1 2X  1  1 3X+2  X  0  1 3X+2  1  2  1  X  1 X+2  X  1 2X  1 3X+2  0  1  1  X 2X+2 X+2  1 2X+2 3X X+2  0 2X  1
 0  1  0 2X 2X+3  3  1  X 3X+3 3X X+3  1  X 3X+1  0  1 2X+2  X 2X+1  1 X+2 2X+3  1 3X+1  X  2  1  1  2  1 2X+2  1 3X+2  1 2X+1 3X+2  1 X+3 3X+2 X+1  1  2 2X+1 3X+3  1  1  1 X+2  0  2 3X 3X+2  X  0
 0  0  1 3X+1 X+1 2X 3X+1 3X  1 2X+1  X  X  1 2X+2 3X+2 X+2  3  1  1 3X+3 3X+1 X+2 2X+3 X+1  2  1 2X+1 2X+2 2X+2 3X+3 X+1  3 2X+3  0  X  1 2X+3 3X+2  1  3 3X+1  1 2X+2 X+3 X+3 2X+3  2 2X  1  1  1  1  1  0

generates a code of length 54 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+86x^50+562x^51+567x^52+852x^53+514x^54+544x^55+316x^56+244x^57+110x^58+182x^59+62x^60+40x^61+2x^62+8x^63+4x^64+1x^68+1x^72

The gray image is a code over GF(2) with n=432, k=12 and d=200.
This code was found by Heurico 1.16 in 0.188 seconds.